RESISTIVITY OF METAL WIRE
AS A FUNCTION OF
TEMPERATURE
Mike L. Meier and Rita Kirchhofer
Department of Chemical Engineering and Materials Science
University of California, Davis
Davis, California 95616
Telephone: 530-752-5166
e-mail: mlmeier@ucdavis.edu
e-mail: rkirchhofer@ucdavis.edu
RESISTIVITY OF METAL WIRE AS A FUNCTION OF
TEMPERATURE
Mike Meier, Rita Kirchoffer
Department of Chemical Engineering and Materials Science
University of California, Davis
Abstract
An experiment has been developed in which 2 meters of wire is placed in an oven, heated to as
high as 800°C and the resistance is monitored as it cools. This experiment involves the use of a
tube furnace, a simple whetstone bridge, a computer for recording the temperature-resistance data,
and a spreadsheet for analyzing the results. The agreement with the literature on the temperature
dependence is excellent, in spite of the oxidation one observes. The equipment is easy to obtain
and build, and the cost of doing this experiment is only the cost of the wire.
Keywords: resistance, resistivity, metals, wire
Prerequisite Knowledge: Ohm’s law, wheatstone bridge, resistance and resistivity
Objectives: Observe changes in resistance in metals wires as a function of temperature and
relate the results to the material’s resistivity.
Equipment and Materials: 2 meters of 18-28 gage wire, tube furnace capable of reaching
800°C, K-type thermocouple and reference junction, wheatstone bridge, basic hand tools such as
pliers and wire cutters, alcohol and cotton gloves for handling the wire, data acquisition system
and software, spreadsheet program such as Microsoft Excel or Corel Quattro Pro.
Introduction: The ability of materials to conduct electric charge gives us the means to invent an
amazing array of electrical and electronic devices, especially considering the extraordinarily
wide range of conductivity available, with insulators on one end and superconductors on the
other. (Semi-conductors, thermoelectric materials, opto-electronic materials and magnetoresistive materials are whole other matters) Between these extremes are materials which offer a
small degree of resistance to flow of electrons, such as ordinary copper wire used in household
wiring, nichrome heater wire used in toasters and ovens, and many other useful materials. This
experiment focuses on the resistance of wires made of materials such as copper and nichrome, or
more specifically, the resistivity of copper and nichrome as functions of temperature.
Conductivity – The electrical conductivity of materials is generally expressed by the equation
(1)
where n is the number of charge carriers, q is the charge of the ion, electron or hole, and : is the
mobility of the charged species. The value of q is either the charge of an electron or a hole, but
may be several times that if the charge is carried by multivalent ions.
Resistivity – The resistivity of materials is simply the inverse of the conductivity
(2)
and the temperature dependence of resistivity is often represented by the empirical relationship
(3)
where D0 is the resistivity at a reference temperature, usually room temperature, and " is the
temperature coefficient. Typical values of D0 and " are listed in table 1 along with the calculated
resistivity at 100°C.
Table 1. Resistivity values of common metals [1]
"
microohm@cm
microohm@cm
/K Note 1
Resistivity at
100°C
microohm@cm
Aluminum
2.284
0.0039
3.064
Copper, Annealed
1.7241
0.00393
2.5101
Copper, Hard Drawn
1.771
0.00382
2.535
Brass
7
0.002
7.4
Gold
2.44
0.0034
3.12
Iron
9.71
0.00651
11.012
Lead
20.648
0.00336
21.32
Nickel
11
0.006
12.2
Silver
1.59
0.0038
2.35
Steel
10.4
0.005
11.4
Nichrome
100
0.0004
100.08
Platinum
10
0.003
10.6
Tungsten
5.6
0.0045
6.5
Material
D0
Note 1. Determined at 25°C
In metals, where the valence electrons easily move in and out of the conduction bands, the
number of charge carriers n is large. Resistivity in metals is therefore more a function of the
mobility of the electrons. In a perfect crystalline lattice the electrons are accelerated by an
electric field and move with very little difficulty. Even in a pure material, thermal oscillations of
the atoms will scatter these moving electrons., increasing the resistivity somewhat. Impurity
atoms and defects such vacancies, dislocations, twin and grain boundaries, will scatter these
electrons even more. The combined effect of thermal, impurity, and defects on the resistivity is
given by Mathesson’s rule where
(4)
For pure elements the contribution of defects is on the order of 0.1 percent of the total but for
heavily cold worked metals it can be as high as 5 percent.
Resistance – Resistance is an extrinsic property of a device which is represented by the equation
(5)
where A is the cross-sectional area and l its length. Practical devices are manufactured using a
number of techniques and geometries, including:
•
Winding a metal wire on a cylindrical ceramic core. These resistors generally have a
high power ratings.
•
Coating a cylindrical ceramic core with a material that has the desired resistivity.
Controlling the film thickness and length (the film may be applied in a helical pattern) is
critical.
•
Applying a thin film of a material with the desired resistivity to a flat ceramic substrate.
After firing or curing this film can be laser “trimmed” to obtain a more precise resistance.
This method is used to put many resistors on a single SIP or DIP resistor package.
In practical applications the temperature dependence of the resistance of a device may be an
issue. When selecting a resistor for use in a circuit one can specify this the thermal tolerances
along with its resistance value and power rating.
Figure 1 On the left are a number of different types of resistors, including c,¼, and 1 watt axial resistors, single and
dual in-line networks, precision wire wound resistors and four tiny surface mount resistors. On the right is a magnified
image of a couple of the carbon film resistors in SIPs and DIPs like those shown on the left. The little “hats” are laser
trimmed to obtain a resistance within 2% of the desire value.
Figure 2 Connection diagram for the data. acquisition system. The numbers 1, 2, and 3
on the DMM refer to the A/D channels.
Procedure: Students prepare to do the experiment by building a simple model/simulation using
spreadsheets or similar software tools. This involves calculating:
•
•
•
Calculating the resistivity of all of the materials listed in table 1 from room temperature
to 1000°C and examining the range of values and the trends.
Calculating the resistance of these materials when they are in the form of 2 meters of 24
gage wire.
Calculating the output voltages from Wheatstone bridge where R1=R2=1000 ohms, R3=1
ohm, and the lead resistance is zero.
When this part of the experiment is done the students will know exactly what to expect when
they do the experiment.
The experiment itself begins by preheating the tube furnace to a suitably high temperature, such
as 800°C, but not high enough to melt the sample. Next, the data acquisition system is set up
and the leads to the Wheatstone bridge are shorted to find the lead resistance. The system is then
tested using several low-resistance (0.5 to 2 ohms) resistors. Figure 2 shows how the equipment
is connected.
The sample is prepared by cutting a two meter length of wire, straightening it, measuring its
length, cleaning it using alcohol, and wrapping it around a small diameter rod. The coiled wire
is then carefully slipped over a slightly larger diameter ceramic tube, making sure the coils do
Figure 3 Top: the basic equipment setup includes a tube furnace, multimeter/scanner,
wheatstone bridge, thermocouple, and computer. Bottom: the sample probe consists of the
wire coiled a round a small diameter ceramic tube with is inserted into the larger ceramic
tube.
not touch each other. A thermocouple is inserted in this tube and this assembly is placed inside
another ceramic tube. Figure 3 shows the completed assembly and the equipment setup.
The thermocouple and wire are connected to the data logging system and the ceramic tube/wire
assembly is inserted into the tube furnace. Once the sample assembly reaches the desired
temperature it is removed from the furnace, placed on a heat resistance surface, and the data
acquisition software is immediately started. The data acquisition software will record and plot
temperature versus resistance. Figure 4 shows a screen shot of the data acquisition software and
the last page in this manuscript is a sample printout.
Once the sample assembly has cooled it can be safely disassembled and the wire inspected for
excessive oxidation, shorting, or other potential problems.
The data is then imported into a spreadsheet where it is plotted and analyzed. From the
measured resistance and wire dimensions the values of D0 and " can be determined. Figure 5
shows the results from this experiment on brass wire. In this case the reference values for D0 and
Figure 5. Typical results from an experiment conducted on a 2.5 meter length of 28 gage copper wire.
" are 1.72 :S@cm and 0.0039 :S@cm/K respectively. The measured values were 2.18 :S@cm
and 0.0038 :S@cm/K. The slight differences could be easily explained in terms of lead
resistance or lower temperature of the wire than the thermocouple. These results were better
than what many students could get. In most cases the values of " was in excellent agreement
with the literature but the value of D0 was several ohms off.
Comments:
The overall results teaching this experiment have been good. Students have commented on how
well the results agree with the values in the references, in spite of the errors due to the
temperature gradient, and simple setup used. They also said they were happy to finally get a
change to work with the wheatstone bridge, and I think they learned more about how to design
and carry out experiments that at first may have seemed difficult.
Students may (should) express some concern about the oxidation of the wire and how it might
have effected the results. In general, it has not been much of a problem so far. Keeping the wire
clean probably helps improve the results of the experiment, but it definitely improves the
students’ confidence in the results.
The issue of temperature gradient, both along the length of the sample assembly and between the
wire and the thermocouple, and has been dealt with as much as possible for this type
(inexpensive) of experiment. In an earlier version of this experiment where we did not use the
outer ceramic tube the difference in temperature between the thermocouple and the wire was
considerable. The result was a value of D0 that was obviously in error but the value of " was
very close to that listed in the references. By using the outer ceramic tube the temperature
should be much more uniform, even if the heating and cooling rates are much lower.
There are a few other practical aspects to consider when doing this experiment. The
temperature-resistance data is recorded during cooling because the fields produced inside the
tube furnace cause problems with the resistance measurements. Collecting the data during
cooling is also slower and so the temperature gradients will be even less of a problem. Also,
having only one tube furnace for four computers and multimeters, the furnace is not as much of a
bottleneck to being able to test a number of samples during the laboratory session. Recording
the data during cooling will also help minimize artifacts caused by recrystallization of the wire,
which is usually heavily cold worked.
The process of selecting which wire to work with can make the experiment interesting. One can
easily find copper, brass, aluminum, and iron wire at the hardware store, and nichrome and other
materials can be obtained from industrial and scientific supply vendors. Nichrome has excellent
oxidation resistance and a high overall resistivity, but a very low value of ". Copper has low
overall resistivity, so low it may be difficult to measure, but its thermal coefficient is about
average. Aluminum has about 50% higher resistivity than copper but it also has a relatively low
melting point compared to the other materials. Brass wire, which has a noticeably higher value
of D0 and a fairly typical value of ", has worked very well in our experiments.
The cost of setting up and running this experiment were modest. We’re using the same
computers and digital multimeter/scanner we use in the phase diagram experiments, and the
software was based on the software used in that experiment. The thermocouple and reference
junction were also laying around the laboratory. The only new parts were the ceramic tubes and
the wheatstone bridge. The wheatstone bridge contains about $25 in parts plus the circuit board
which was designed on my computer using ExpressPCB’s free software and then manufactured
by ExpressPCB for a cost of about $25 per board. The cost of the wire, which was purchased at
the local hardware store, is negligible.
References:
1. CRC Handbook of Chemistry and Physics, 65th edition, CRC Press, Inc, Boca Raton, FL, pp.
F-114 - F-120, (1984-85).
Biography:
Michael L. Meier received his B.S. in Materials Engineering from North Carolina State
University in 1979 and his M.S. (1986) and Ph.D. (1991) in Materials Science and Engineering
from the University of California, Davis. After a two-year post-doctorate position at the
Universität Erlangen-Nürnberg in Erlangen, Germany he returned to UC Davis where he is now
the director of Materials Science Central Facilities and is also developing the laboratory teaching
program.
Rita Kirchhofer is an undergraduate student at the University of California, Davis seeking
degrees in Mechanical Engineering and Materials Science and Engineering. She has participated
in the Materials Science Internship Program set up by Michael Meier at her institution for two
years. This is her second collaboration for the N.E.W. Conference.
Appendix 1. AWG wire gages
Wire Gage
Diameter in mils at
20°C
Diameter in
millimeters at 20°C
8
128.5
3.26
10
101.9
2.59
12
80.81
2.05
14
64.08
1.63
16
50.82
1.29
18
40.30
1.02
20
31.96
0.81
22
25.35
0.64
24
20.10
0.51
26
15.94
0.40
28
12.64
0.32
30
10.03
0.25
32
7.950
0.20
34
6.305
0.16
Appendix 2. Wheatstone Bridge
This experiment uses a standard wheatstone bridge. In the circuit used here RA and RB serve as
current limiting resistors for cases where R and R3 are low, such as during a short circuit when
configured to measure low values of R. The circuit diagram and layouts are shown in figures 6
and 7.
Figure 6 This circuit is a standard wheatstone bright that has two
current limiting resistors (RA and RB) and a selection or resistors R3-1 R3-5) that allows one to select the best resistance range.
Figure 7 The circuit board for the wheatstone bridge was designed
using ExpressPCB’s free software. The file was uploaded to
ExpressPCB who made the boards.
Circuit Equations
VS is the voltage of the power source, such as a battery and is typically 1.5 volts. Higher
voltages can lead to high current passing through the 1 - 2 ohm resistor being measured. All
resistor values are in ohms.
Appendix 3. Safety Considerations
Chemical Hazards
The methanol used to clean the wire poses fire and health hazards.
Handle this solvent carefully. Use only small quantities, clean up
any spills immediately, and keep it and its fumes away from the
hot furnaces. An MSDS for methanol can be provided on request.
Physical Hazards
Burns – The temperatures used in this experiment can cause
serious burns and even fires if flammable materials come in
contact with the hot parts. Be extremely careful when working
with the furnaces and the hot specimens, be careful and deliberate
when removing and handling the hot specimens, and remember,
parts do not have to be glowing to be very hot.
Electrical – There is a minor electrical hazard in this experiment,
similar to that one ... with when dealing with any small electrical
appliance.
Fire – The combination of high temperatures, electrical appliances,
and flammable methanol presents a definite fire hazard. Keep the
methanol away from the furnaces, clean up any spills immediately
and work with on small quantities of this flammable solvent.
Biohazards
None.
Radiation Hazards
None.
Protective Equipment
Recommended: safety glasses
Required: heat-resistant gloves, as needed
Resistivity 1.0
Resistance-Temperature Recording for the Keithley 199 DMM/Scanner
Version: 1.0 alpha, October 24, 2002
Project
Name: Resistivity 1.0
Description: Resistance-Temperature Recording for the Keithley 199 DMM/Scanner
Owner: K Street Technology Center
Data File: Resistivity10.csv
Sensor Parameters
Thermocouple Type: K
Resistance RA: 10.00 ohms
Resistance R1: 1000.00 ohms
Resistance R3: 1.00 ohms
Resistance VS: 1.50 volts
Resistance RB: 10.00 ohms
Resistance R2: 1000.00 ohms
Resistance RL: 0.00 ohms
DMM/Scanner Parameters
DMM Status String: n/a
Function: DC Volts
Range: 300 mV
Resolution: 4½ digits
Channel 1: Temperature
Channel 2: V0
Channel 3: Resistance
Sampling Parameters
Period: 1 second
Channels Scanned: 1 through 3
Start Time: 09/02/04, 22:47:41
End Time: 09/02/04, 22:48:26
Duration: 0:00:45 (45.4 s)
Samples: 47
Comments
Sample Data
Resistance-Temperature Recording for the Keithley 199 DMM/Scanner
NEW Update 2004
3.00
2.40
Resistance, ohms
1.80
1.20
0.60
0.00
0
80
160
240
Printed on Thursday, September, 2, 2004, 10:49:00 pm
320
400
Temperature, °C
480
560
640
720
800